I use munin, the monitoring program, to alert me by email when something goes wrong on my server.
It sends emails as munin.

Normally, when an email like this is to be delivered on the Internet, when postfix/cleanup is called, it asks trivial-rewrite to do a rewrite, which should append realdomain.tld to incomplete sender address.

It seams it does not, because my Postfix SMTP client then tries to send the email containing the From: munin@thehostname header, which Google doesn't really like:

Yes I use procmail, but I think this program is only called for local delivery (like for the bounce message which was sent to munin@thehostname). But for the email I'm talking about qmgr gave it to smtp, not to local process.
–
FoxJul 22 '13 at 19:12

I just edited my post to add more information.
–
FoxJul 22 '13 at 20:10